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VITEEE 2017 Paper

Section: Physics

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Question : 33 of 125

Marks: +1, -0

Resonance frequency of LCR series a.c. circuit is

f_0

. Now the capacitance is made 4 times, then the new resonance frequency will become

$f_0$ /4
2 $f_0$
$f_0$
$f_0$ /2

Solution:

In LCR series circuit, resonance frequency

f_0

is given by

Lω =

\frac{1}{C\omega}

⇒

\omega^2

=

\frac{1}{LC}

∴ ω =

\sqrt{\frac{1}{LC}}

=

2\pi f_0

∴

f_0

=

\frac{1}{2\pi\sqrt{LC}}

or

f_0

α

\frac{1}{\sqrt{C}}

When the capacitance of the circuit is made 4 times, its resonant frequency become

f_0

∴

\frac{f_0'}{f_0}

=

\frac{\sqrt{C}}{\sqrt{4C}}

or

f_0'

=

\frac{f_0}{2}

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